Originally Posted by: I was reading something online and it said how some musicians utilize serial composition in their music or serialism. What is serialism? Also, what is retrograde and retrograde inversion and could you give an example? I'm very curious as to what these terms mean. Thank you, it is appreciated.
Serial composition is a way of organizing reoccurring elements of music (such as melody or harmony) in a way that gives a piece unity. Serialization is not a style or a way of composing, but it is a technique of composing. It is often used in 12-tone music, and a great example of it would be Arnold Schoenberg's work.
Serial composition utilizes what are called "pitch classes" and "pitch sets," which put simply means that a number is assigned to each pitch based on their organization within the pitch-space (the infinite collection of pitches possible). These are often mathematical relations that yield non-tonal harmony, but it does not necessarily have to be limited to non-tonal harmony, as tonal harmony is actually often described as a subset of the total collection of the pitches.
An example of a subset collection is actually the "Circle of fifths," which is an organization of the total set of pitches described by sets of 7 in relation to their most direct modulation between nearest key centers. It only takes one note-change to move from G to C or from G to D, and so on. Thus the circle of fifths provides an organizational tool that provides a method of moving between keys in an musically coherent way. This is a simple example of serialization because serialism takes this concept and applies it to different collections and pitch-sets, not just the tonal scales that we are used to. This example would be applicable if one used the circle of fifths two move from a specific point on the circle two another specific point on the circle as a part of one's organization of the composition. Like if you moved from C through the 12 different keys back to C every twelve bars, that would be a small use of serialism in tonal music.
Retrograde Progressions in tonal music on the other hand is a type of progression. Normal progressions typically have tonic, preparatory chords, dominant, tonic. This is the typical motion in most tonal music, but there is a tool called retrograde which yields interesting results, which means you reverse this sequence: tonic, dominant, preparatory chords, tonic. For example: I IV V I (standard), I V IV I (Retrograde). Because the nature of the dominant-tonic relationship, the ear wants/expects the tonic to follow, and so by delaying the tonic resolution by placing other chords in its way (like the ii, IV, etc), than the progression becomes retrograde, and gives you a different emotion than what the normal progression. A I IV V usually sounds happy, where as a I V IV I sounds almost melancholy. Same chords, but different order.
Yet there is a retrograde that can be applied to rhythm (a backwards rhythm of an earlier used rhythm).
There is also a retrograde that applies to serialism, which is where the ordered series of pitches that I talked about earlier is reversed. So if the composition made its way, for example, linearly up the chromatic scale for the first half of the composition, a retrograde of that would descend down the chromatic scale during the second half. Yet don't misunderstand the simple example: this does not mean simply going up and down a scale, but a reversal of the melody and harmonic elements. You can think of it this way: like a mirror was placed on the sheet of music paper and created the next section of the music. This is probably what you meant more by what is retrograde, but I included the tonal retrograde progression answer as well, because it is more directly applicable to most musicians.
Retrograde inversion is taking the organized series of pitches and not only reversing it, but inverting it as well. This is not as simple as the "mirror' example, because inverting involves a particular pitch around which pitches are mathematically mapped from one pitch to the next. It is more involved than reversing the organization, it takes a deeper understanding of how the organization of pitches works, which would require a much deeper exploration. Inversion does not necessarily mean flipping it upside down, even though that is what the name implies, because you could invert the music around any point on the collection.
I hope I did not confuse you further, because these topics are very expansive and mathematically-heavy, so I hope you were able to glean some understanding. If you have further questions, I would be happy to make things more clear as your understanding of these dense topics unfolds.